Well, you CAN freeze just about anything - may not be worth eating when defrosted though! In this case, fruit cake - definitely. Iced sponge- perhaps, but the icing will fall off when defrosted.
You can freeze both. The icing on the birthday cake may be a wee bit grainy after freezing but it is possible to do. I freeze iced cupcakes and they defrost absolutely fine.
When MOH did lots of cooking she baked the Chrismas cakes for the whole family in the spring and then froze them until the following Decenber. Although she did make one daughters wedding cake (4 tiers) three years before the chap had even asked!!
You can freeze fruit cake/Loaf. But, when you defrost it, leave it in the wrapping you have frozen it in and defrost for about three hours. That way, you would not know it had been frozen, it tastes as fresh as if you had made it on the day you defrosted it.